KR19990010106A - Method and apparatus for data storage in parity storage and disk failure in external storage subsystem - Google Patents

Abstract

The present invention relates to an efficient disk distribution scheme (referred to as a DH scheme in the present invention) using diagonal parity and horizontal parity. The DH scheme according to the present invention is a technique for repeatedly applying diagonal parity and horizontal parity even if an error occurs in two disks arbitrarily in a disk array having N prime numbers. In the case of constructing a disk array with N disks, each disk is defined by (N-1) * N matrix composed of (N-1) blocks, the horizontal parity blocks are arranged diagonally on each disk, The blocks are located in the (N-1) th block of each disk. In the parity storing method, the data values of the error correction group are subjected to XOR (eXclusive OR) operation and stored in the parity block of the group. When an error occurs in the two disks, a block is first recovered by applying a diagonal parity group Then, it is used to recover the error occurrence block of the horizontal parity group, and it is possible to recover the blocks of all erroneous disks when the process is repeatedly applied.

Description

Method and apparatus for data storage in parity storage and disk failure in external storage subsystem

The present invention relates to an external storage subsystem, and more particularly, to a method and apparatus for performing parity storage and thus data recovery in order to facilitate data recovery in a disk failure in a disk array.

Recently, with the development of semiconductor technology, faster and more powerful microprocessors and memories have been developed, but the performance of hard disks with mechanical characteristics is not enough. In other words, the RISC (Reduced Instruction Set Computer) microprocessor shows a performance improvement of more than 50% every year, while the access time of the hard disk is less than 10% per year. Therefore, performance degradation of I / O subsystem based on hard disk is an important reason to limit the performance of the whole system.

Patterson et al. (A) published a report titled A Case for Redundant Arrays of Inexpensive Disks (RAID) on pages 109 to 116 of a report issued by ACM SIGMOD Conf. In 1988 in Chicago, USA. The RAID presented in this report discloses six levels of disk arrays, from level 0 to level 5, depending on their structure and characteristics. Six RAID levels (level 0 to level 5) have advantages and disadvantages for each shell-like environment and are used in various applications. These RAIDs not only guarantee high performance by enabling parallel processing of disk arrays, but also have reliability characteristics that can be recovered even when a disk error occurs due to redundancy and have large capacity because they are composed of a plurality of disks.

However, as the characteristics of multimedia data as well as the existing document type data are accelerated, a space for storing more data is needed, so that it is a reality that the number of disks constituting the disk array can not be increased any more. However, the probability of disk read failure becomes higher as a large-capacity disk array is constructed. If MTTF (Mean Time To Failure) is the average time that can occur in a single disk, the average time for error occurrence is simply MTTF / n when the number of disks constituting the disk array is n. Therefore, even if the number of disks constituting a disk array is increased, a method of ensuring high reliability can be realized by the conventional RAID having redundancy to recover only one disk error, RAID level 6 is often required. RAID level 6 is described in ACM Computing Surverys, vol. 26, pp. 109-116, a report titled RAID: High-Performance, Reliable Secondary Storage. Another reason to ensure high reliability is that errors on the disk can be more likely to occur due to system failures, uncorrectable bit errors, and other reasons. Level 6, defined by Patterson et al., Uses reed solomon code, which is expensive due to the complexity of the code and requires additional hardware.

On the other hand, there are two-dimensional parity scheme and EVENODD scheme and a redundancy matrix scheme which are recently proposed.

The two-dimensional parity technique is described in Computer Science Tech. Report CSD88-477, Univ. in Patterson et al., entitled " Coding Techniques for Handling Failures in Large Disk Arrays, " The two-dimensional parity scheme extends the structure of the RAID level 4 and places the parity disk not only in the horizontal direction but also in the vertical direction. However, this two-dimensional parity scheme has the following two problems. The first is that the parity disk is not distributed, which can lead to bottleneck of the parity disk, which is a main cause of system performance degradation. The second is that the parity disk overhead is large.

The EVENODD technique is described by Blaum et al. In IEEE Trans. on Computers, vol. 44, no. 2, pp. In the paper titled EVENODD: An Efficient Scheme for Tlating Double Disk Failures in RAID Architectures, The greatest feature and advantage of the EVENODD technique is that it uses an optimal parity disk. That is, if a prime number m disk is used as a data disk, the parity disk overhead is optimal because only two parity disks are additionally used. However, as with the two-dimensional parity scheme described above, the EVENODD scheme has a problem that the performance degradation due to the bottleneck phenomenon is predicted and the average time (MTTDL: Mean Time To Data Loss. Another disadvantage of the EVENODD scheme is that there is an overhead for maintaining each of the oblique data blocks. That is, when a write operation is performed on data blocks of oblique blocks of each disk, the values of all the blocks of the oblique parity disk are changed, so that it is an example of the overhead to update all the blocks.

U.S. Patent No. 5,271,012, entitled " METHOD AND MEANS FOR ENCODING AND REBUILDING DATA CONTENTS OF UP TO TWO ", filed 14 December 1993, invented and patented by Blaum et al. UNAVAILABLE DASDS IN AN ARRAY OF DASDS) and U.S. Patent No. 5,351,246 issued September 27, 1994 (entitled METHOD AND MEANS FOR CODING AND REBUILDING THAT DATA CONTENTS OF UNITEDABLE DASDS IN ERROR IN THE PRESENCE OF REDUCED NUMBER OF DASDS) UNIVEAILABLE DASDS IN A DASD ARRAY has been disclosed to encode a disk array using diagonal parity and row parity, and to recover even if an error occurs in two disks. However, both of these patents 5,271,012 and 5,351,246 have disadvantages in the EVENODD technique.

A technique using a redundant matrix is disclosed in IEEE Trans. on Parallel and Distributed Systems, vol. 6, no. 11, pp. 1177-1184, entitled Efficient Placement of Parity and Data to Tolerate Two Disk Failures in Disk Array Systems. In order to solve the bottleneck problem of the parity disk inherent in the methods such as the two-dimensional parity method, the method using the redundant matrix is a method of distributing parity blocks. When N disks are given, If the matrix is defined as a matrix and the matrix meets some characteristics, data can be recovered in the event of an error in two disks. This technique has the advantage of solving the bottleneck caused by the overhead on the parity disk which is problematic in other techniques by distributing the parity and data blocks by the placement algorithm. However, the complexity of the algorithm and the overhead The head and additional cost can be a problem. In addition, there is a problem that the algorithm must be deployed again when expanding.

It is therefore an object of the present invention to provide a method and apparatus for solving the problem of performance degradation due to a bottleneck of a parity disk, even if an error occurs in at least two disks in a disk array.

It is another object of the present invention to provide a method and apparatus for reducing recovery time in the event of a disk error.

It is still another object of the present invention to provide a method and apparatus for overcoming performance degradation due to multiple disk accesses at the time of updating the contents of a data disk.

It is still another object of the present invention to provide a method and apparatus for concurrently performing a disk error recovery process.

According to another aspect of the present invention, there is provided a method for restoring parity storage and disk failures in an external storage subsystem, the method comprising the steps of: allocating a small number of N disks and each disk of the disks to (N-1) (N-1) * N matrix, blocks of each row of the matrix are defined as a horizontal parity group, blocks of a recursive configuration in the upper right diagonal direction of the matrix are defined as a diagonal parity group (N-1) -th block of the disk, and the horizontal parity blocks are arranged in the oblique direction on the first block of the immediately preceding (N-1) -th disk, and the oblique parity blocks are arranged in the A process; A parity storing step of performing XOR operation on the data values of each of the horizontal and diagonal parity groups and storing the data values in the horizontal and diagonal parity blocks of the corresponding group; If an error occurs in the two disks, restores the fail block using a diagonal parity group including one fail block, and then restores the fail block of the horizontal parity block using a horizontal parity group of the recovered fail block, And restoring the fail blocks of the two failed disks by repeatedly applying the above process.

(N is a prime number) disks and each disk of the disks is divided into (N-1) block units. The method of claim 1, (N + 1) th row, and blocks of each row of the matrix are defined as a horizontal parity group, and blocks of the last (N + 1) th disk are excluded (N + 1) -th disk, blocks of sloping parity are defined as (N-1) -th block of the disk, and blocks of the cyclic configuration are defined as a sloped parity group. 1) th blocks; A parity storing step of performing XOR operation on the data values of each of the horizontal and diagonal parity groups and storing the data values in the horizontal and diagonal parity blocks of the corresponding group; If an error occurs in the two disks, restores the fail block using a diagonal parity group including one fail block, and then restores the fail block of the horizontal parity block using a horizontal parity group of the recovered fail block, And restoring the fail blocks of the two failed disks by repeatedly applying the above process.

1 is a block diagram of a disk array block implemented by a DH technique according to an embodiment of the present invention;

2 is a block diagram of a disk array block implemented by the DH2 technique according to another embodiment of the present invention;

3 is an exemplary diagram for explaining horizontal and diagonal parity groups and horizontal and diagonal parity blocks according to the DH scheme,

4 is an exemplary diagram for explaining horizontal and diagonal parity groups and horizontal and diagonal parity blocks according to the DH2 technique,

FIG. 5 is a diagram illustrating the arrangement of horizontal parity groups and horizontal parity blocks of the DH scheme when the number N of disks is 7;

6 is a diagram illustrating the arrangement of a diagonal parity group and a diagonal parity block of the DH scheme when the number N of disks is 7;

FIG. 7 is a diagram illustrating parity and data arrangement in the DH scheme when the number N of disks is 7; FIG.

8 is a diagram illustrating the arrangement of horizontal parity groups and horizontal parity blocks of the DH2 scheme when the number N of disks is 7,

9 is a diagram illustrating the arrangement of a diagonal parity group and diagonal parity blocks of the DH2 scheme when the number N of disks is 7;

10 is a diagram showing parity and data arrangement in the DH2 scheme when the number N of disks is 7;

11 is a flowchart of a parity storage algorithm according to the DH scheme, which is an embodiment of the present invention.

FIGS. 12 to 14 are diagrams for explaining a parity storing process according to the DH scheme when the number N of disks is 7,

15 is a flowchart of a parity storing algorithm according to the DH2 technique, which is another embodiment of the present invention;

16 to 18 are diagrams for explaining a parity storing process according to the DH2 scheme when the number N of disks is 7,

FIG. 19 is a flowchart of a decoding algorithm of a DH scheme when two disks fail according to an embodiment of the present invention; FIG.

FIGS. 20A to 20G are diagrams for explaining a data restoration process according to the DH scheme when two disk failures are generated; FIG.

21 is a flowchart of a decoding algorithm of the DH2 technique according to another embodiment of the present invention,

FIGS. 22A to 22G are diagrams for explaining a data restoration process according to the DH2 scheme when two disk failures are generated; FIG.

23 is an exemplary diagram for explaining the parallelism of the error recovery method according to the embodiment of the present invention,

Figure 24 is a graph of MTTDL comparisons for each technique,

FIG. 25 is a diagram showing parity blocks (when N = 7) to be accessed when an oblique line S block is updated in the EVENODD scheme,

26 is a diagram showing parity blocks (when N = 7) to be accessed in data block updating in the DH scheme,

Figure 27 is a group size comparison graph for each technique.

The DH scheme according to the embodiment of the present invention is an efficient parity placement technique that can recover only two XOR (eXclusive OR) operations even when two disks fail, and eliminates the bottleneck by distributing parities, thereby improving the performance of the disk array . It should be understood that in the DH scheme, D and H are derived from the English header of diagonal parity and horizontal parity.

Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. It is to be noted that the same components and the same components as those in the drawings are denoted by the same reference numerals or the same reference numerals as possible. In the following description, well-known functions or constructions are not described in detail since they would obscure the invention in unnecessary detail.

In the following description of the present invention, a DH scheme, which is a temporary example of the present invention, will be described with reference to Figs. 1, 3, 5 to 7, 11 to 14, 19, 20A to 20G, The DH2 technique, which is another embodiment of the present invention, will be described with reference to Figs. 2, 4, 8 to 10, 15 to 18, 21, and 22a to 22g.

First, the DH technique, which is a temporary example of the present invention, will be described with reference to Figs. 1, 3, 5 to 7, 11 to 14, 19, and 20A to 20G.

DH technique

1 is a block diagram of a disk array implemented by the DH technique according to an embodiment of the present invention. Referring to FIG. 1, a host computer 2 sends an I / O request to a controller 4 of a disk array and processes data. The controller 4 includes a unit that implements an encoding and decoding algorithm of the DH technique, and a processor that can mainly perform an XOR operation, for overall processing, management, and maintenance of the disk array. Data blocks and parity blocks based on the structure of the DH scheme according to the embodiment of the present invention are configured in each disk of the disks 8-0 to 8- (n-1) composed of N (N = prime) numbers. Buffers 6-0 to 6- (n-1) located between the controller 4 and the disks 8-0 to 8- (n-1) are provided to reduce the disk access time in the controller 4 , And is implemented as a high-performance buffer to improve the system performance of the disk array. The host computer 2 and the controller 4 are connected by the system bus 10 and are connected between the controller 4 and the buffers 6-0 to 6- (n-1), the disks 8-0 to 8- (n-1) 0 to 6 - (n-1) are directly connected to the respective I / O buses 12-0 to 12- (n-1) for high-speed input / output.

FIG. 3 is an exemplary view for explaining horizontal and diagonal parity groups and horizontal and diagonal parity blocks according to the DH scheme, FIG. 4 is an exemplary diagram for explaining horizontal and diagonal parity groups and horizontal and diagonal parity blocks according to the DH2 technique to be.

FIG. 5 is a diagram showing the arrangement of horizontal parity groups and horizontal parity blocks of the DH scheme when the number N of disks is 7. FIG. 6 is a diagram illustrating the arrangement of diagonal parity groups and diagonal parity blocks of the DH scheme, FIG. 7 is a diagram showing the arrangement of parity and data in the DH scheme in the form of a matrix when the number N of disks is 7. FIG.

11 is a flowchart of a parity storage algorithm according to the DH scheme according to an embodiment of the present invention. And FIGS. 12 to 14 are diagrams for explaining a parity storing process according to the DH scheme when the number N of disks is 7.

1, a horizontal parity block and a group (definition 2), and a diagonal parity block (definition 2) of a DH scheme are described with reference to FIGS. 3 and 5 to 7 in an embodiment of the present invention. And a group (Definition 3), and describes the data and the arrangement of the DH scheme based on the above definitions.

Definition 1: Configuration of DH technique

In the case of constructing a disk array made up of a small number N of disks, each disk is made up of (N-1) logical blocks and is defined as an (N-1) * N matrix as follows.

a _{(i, j)}

Here, the range of i is 0? I? N-2 and j is 0? J? N-1. Table 1 below represents the matrix a _{(i, j)} defined above.

a _(0,0) a _(0,1) ... a _{(0, j)} ... a _{(0, N-1)} a _(1,0) a _(1,1) ... a _{(1, j)} ... a _{(i, N-1)} a _(2,0) a _(2,1) ... a _{(2, j)} ... a _{(i, N-1)} ... ... ... ... ... ... a _{(i, 0)} a _{(i, 1)} ... a _{(i, j)} ... a _{(i, N-1)} ... ... ... ... ... ... a _(N-2,0) a _(N-2,1) ... a _{(N-2, j)} ... a _{(N-2, N-1)}

The matrix a _{(i, j)} represents the value of the logical block i of the disk j. In the present invention, each logical block is represented by a binary number. The (N-1) * N matrix of a _{(i, j)} is given to the case (N-1) th row, i.e., the last block of each disk _{a (N-2,0), a} (N-2 _{, 1),} ... _{, A (N-2, N} -1) is deulyigo diagonal parity blocks are used to maintain the diagonal parity, (N-1) th first block is a _{(0, N-2)} last block of the first disk from the disk to a _(N-2,0) That _{is, a (0, N-2} ), a (1, N-3), a (2, N-4), ... _, a _(N-3,1) and a _(N-2,0) are used as horizontal parity blocks for storing the parity values of the respective rows, and the other blocks are data blocks in which data is stored.

Definition 2: Horizontal parity group and block in DH scheme

In the matrix a _{(i, j)} representing the disk array defined in Definition 1, each row is defined as an error correction group of horizontal parity (hereinafter abbreviated as a horizontal parity group), and from the last block of the first disk to the upper right (Hereinafter referred to as a horizontal parity block) up to the first block of the (N-1) -th disk. That is, the parity values of each horizontal parity group are stored in blocks corresponding to the matrix a _{(i, N-2-i)} . Here, the range of i is 0? I? N-2.

FIG. 3 shows a disk array implemented with five disks (N = 5) d0 to d4, whereby each of the disks d0 to d4 includes four logical blocks (N-1 = 4) b0 to b3, b4 to b7, ... . Each of the four logical blocks b0 to b3 is a corresponding horizontal parity group. In FIG. 3, reference numeral 20 indicated by a solid line represents a horizontal parity group of the second block b1 as an example. In FIG. 3, hatched blocks denote horizontal parity blocks storing parity values of each horizontal parity group, and the horizontal parity blocks are blocks corresponding to a matrix a _{(i, N-2-i)} . That is, since N = 5, it can be seen that a block corresponding to a _(3,0), a _(2,1), a _{(1,2), and} a _(0,3) is a horizontal parity block.

FIG. 5 shows each horizontal parity group in the DH scheme in the case of N = 7 in numbers (0, 1, 2, 3, 4, 5). Blocks H0 to H5 indicated by hatched lines are parity Block.

Definition 3: Diagonal parity in the DH scheme Groups and blocks

The (N-1) th row to the (N-1) * N matrix a _{(i, j)} of Definition 1 are blocks (hereinafter referred to as oblique parity blocks) for storing respective diagonal parity values. Each group of error correction groups (hereinafter abbreviated as diagonal parity groups) of diagonal parity is configured cyclically in the oblique direction to the upper right of the oblique parity block as if the horizontal parity blocks are located. The first diagonal parity group among the diagonal parity groups are groups in the upper right diagonal direction of the last block of the first disk. Parity values of each oblique parity group are stored in oblique parity blocks, i.e., blocks belonging to the matrix a _{(N-2, j)} . Here, the range of j is 0? J? N-1.

In FIG. 3, reference numeral 22 indicated by a dotted line indicates an example of a second diagonal parity group. Blocks indicated by black dots located in 4 (= N-1) th rows (i = 3) are diagonal parity blocks storing parity values of each diagonal parity group. FIG. 6 shows each of the slanting parity groups in the case of N = 7, and blocks D0 to D6 indicated by black dots are parity blocks of each slanting parity group.

The remaining blocks excluding the horizontal parity block and the diagonal parity block defined in Definition 2 and Definition 3 are data blocks in which actual data is stored. FIG. 7 is a diagram illustrating parity and data arrangement in the DH scheme in the form of a matrix when the number N of disks is 7. In FIG. 7, H0 to H6 denote horizontal parity blocks of horizontal parity groups (0 to 6), and D0 to D6 denote diagonal parity blocks of diagonal parity groups (0 to 6). Each data block is represented by i, j, where i denotes a horizontal parity group and j denotes a diagonal parity group.

The parity storing algorithm according to the DH method is a method of obtaining a parity value of data blocks in each parity group through an XOR operation. FIG. 11 is a flowchart of a parity storing algorithm of the DH method according to an embodiment of the present invention. When the (N-1) * N disk array is configured as shown in step 100 of FIG. 11, the controller 4 of FIG. 1 performs steps 110 and 120 of FIG. 11 to obtain a horizontal parity value and a diagonal parity value. First, in step 110, a horizontal parity block is encoded using each horizontal parity group 0 to (N-3). More specifically, the controller 4 calculates the horizontal parity values of the corresponding horizontal parity group using the horizontal parity groups 0 to (N-3), and stores them in the corresponding horizontal parity blocks. The horizontal parity value stored in the horizontal parity block is obtained by Equation (1).

After step 110, the controller 4 encodes the oblique parity block using the diagonal parity groups 0 to (N-1) in step 120, respectively. More specifically, the controller 4 calculates diagonal parity values of the oblique parity groups using the oblique parity groups 0 to (N-1), and stores them in the corresponding oblique parity blocks. The diagonal parity value stored in the corresponding slanting parity block is obtained by Equation (2).

An example of calculating an actual horizontal parity value and a diagonal parity value using Equations (1) and (2) will be described with reference to FIG. 12 to FIG. FIGS. 12 to 14 are diagrams for explaining a parity storing process according to the DH scheme when the number N of disks is 7; FIG.

If N = 7, parity storage method according to DH scheme

The matrix shown in Table 2 below shows a matrix representing a disk array of the DH scheme for seven disks, i.e., N = 7, where the blocks in each disk are given matrix numbers to be used in encoding and decoding.

a _(0,0) a _(0,1) a _(0,2) a _{(0, 3)} a _(0,4) a _(0,5) a _(0,6) a _(1,0) a _(1,1) a _(1,2) a _{(1, 3)} a _{(1, 4)} a _(1,5) a _(1,6) a _(2,0) a _(2,1) a _(2,2) a _(2,3) a _(2,4) a _(2,5) a _(2,6) a _(3,0) a _{(3, 1)} a _(3,2) a _{(3, 3)} a _(3,4) a _(3,5) a _(3,6) a _(4,0) a _(4,1) a _(4,2) a _(4,3) a _{(4, 4)} a _(4,5) a _(4,6) a _(5,0) a _{(5, 1)} a _(5,2) a _(5,3) a _(5,4) a _{(5, 5)} a _(5,6)

12 shows a state where arbitrary data of binary numbers are stored in each data block in a matrix expressed by the table 2. The horizontal parity values are displayed in the empty blocks indicated by hatching, The diagonal parity values will be stored after XOR calculation for each group based on Equations (1) and (2).

In the following first the horizontal parity blocks using Equation 1 (i.e., the matrix _{a (0,5), a (1,4} ), a (2,3), a (3,2), a (4,1 ₎ ) Of the horizontal parity value.

a _(0,5) = a _(0,0) a _(0,1) a _(0,2) a _{(0, 3)} a _(0,4) a _(0,6)

= 1 0 One One 0 0 = 1

a _{(1, 4)} = a _{(1, 0)} a _(1,1) a _(1,2) a _{(1, 3)} a _(1,5) a _(1,6)

= 0 One One 0 0 1 = 1

a _(2,3) = a _(2,0) a _(2,1) a _(2,2) a _(2,4) a _(2,5) a _(2,6)

= 1 One One 0 0 0 = 1

a _{(3, 2)} = a _{(3, 0)} a _{(3, 1)} a _{(3, 3)} a _(3,4) a _(3,5) a _(3,6)

= 0 0 One 0 One 0 = 0

a _{(4, 1)} = a _(4, 0 ₎ a _(4,2) a _(4,3) a _{(4, 4)} a _(4,5) a _(4,6)

= 0 0 One 0 One 1 = 1

In FIG. 13, the horizontal parity values a _(0,5), a _(1,4), a _(2,3), a _{(3,2) , and} a _(4,1) , respectively. Of the matrix a _(0,5) horizontal parity block 1, the matrix a _(1,4) horizontal parity block 1, the matrix a _(2,3) horizontal parity block 1, the matrix a _(3,2) of the 0 is stored in the horizontal parity block, and 1 is stored in the horizontal parity block of the matrix a _{(4, 1)} .

_(5,0), a _(5,1), a _(5,2), a _{(5,3), and} a _(5,4) using the equation (2 _{) ,} a _{(5, 5)} ).

a _(5, 0 ₎ = a _{(4, 1)} a _(3,2) a _(2,3) a _{(1, 4)} a _(0,5)

= 1 0 One One 1 = 0

a _(5,1) = a _(4,2) a _{(3, 3)} a _(2,4) a _(1,5) a _(0,6)

= 0 One 0 0 0 = 1

a _(5,2) = a _(4,3) a _(3,4) a _(2,5) a _(1,6) a _(0,0)

= 1 0 0 One 1 = 1

a _(5,3) = a _(4,4) a _(3,5) a _(2,6) a _(1,0) a _(0,1)

= 0 One 0 0 0 = 1

a _{(5, 4)} = a _{(4, 5)} a _(3,6) a _(2,0) a _(1,1) a _(0,2)

= 1 0 One One 1 = 0

a _{(5, 5)} = a _{(4, 6)} a _(3,0) a _(2,1) a _(1,2) a _{(0, 3)}

= 1 0 One One 1 = 1

a _(5,6) = a _(4,0) a _{(3, 1)} a _(2,2) a _{(1, 3)} a _(0,4)

= 0 0 One 0 0 = 1

In FIG. 14, the horizontal and the diagonal parity values are obtained through the above process, and then stored in the respective horizontal and diagonal parity blocks. That is, FIG. 14 shows an example of parity and data arrangement according to the embodiment of the present invention when N = 7.

Next, a method of decoding a DH scheme according to an embodiment of the present invention, that is, a method of recovering data on a disk in the event of a disk error, will be described.

The basic idea of the data recovery method of the corresponding disk according to the DH method is as follows. When one disk fails, it can be easily recovered by using horizontal parity or diagonal parity. When an error occurs in two disks, the oblique parity and horizontal parity are repeatedly applied And recover all the blocks on both disks. In a disk array made up of a few N blocks, when only one block in a horizontal parity group is erroneous, the remaining blocks can be recovered by XORing. That is, when (N-1) blocks of the N blocks constituting the horizontal parity group are complete, a block of the erroneous disk can be recovered.

A diagonal parity group consists of (N-1) blocks, which are distributed on different disks. Due to such a distributed structure, even if two of the N disks fail, at least one error occurs in only one block among the oblique parity groups. Therefore, if the block is restored, the rest of the N blocks of the horizontal parity group including the block can be restored. Since the restored one block is again one block of the oblique parity group, the rest of the failed parity blocks of the oblique parity group can be recovered and applied to all the blocks in the same manner. In this way, it is possible to recover all errors in any two disks in a disk array made up of a few N pieces.

19, when a disk i and a disk j fail, k is obtained as a disk difference value, and then a disk j (i + 1) belonging to a diagonal parity group of a diagonal parity block of the disk i + Lt; / RTI > Then, the block of the disk i is recovered through the horizontal parity group including the block of the disk j, and the process is repeatedly performed to recover all the blocks of the failed two disks.

A method of recovering all blocks of a corresponding disk in which an error occurs in the controller 4 of FIG. 1 according to an embodiment of the present invention when an error occurs in two disks will be described in detail with reference to FIG. FIG. 19 is a flowchart of a decoding algorithm of a DH scheme when two disks fail according to an embodiment of the present invention. FIG. In Fig. 19, the following assumption is made.

Assumption: Error occurred on disk i and disk j (0? I <j? (N-1)

The controller 4 of Fig. 1 sets k = j-i and m = 0 in step 300 of Fig. That is, when the disk i and the disk j fail, k is obtained as a difference value of the disk, and a variable m for initializing the block restoring process of the failed disks is initialized to zero.

Then, in step 302, the following n value is obtained.

n = N-1-k-m * k mod N

As described above, the diagonal parity group is composed of (N-1) blocks, which are distributed on different disks. Therefore, even if there are errors in two disks in N disks, there is at least one error occurred in only one of the oblique parity groups. Therefore, n is a value indicating a fail block of the disk j of the diagonal parity group in which only one block of error has occurred. In step 304, the controller 4 decodes the block n of the disk j using the slant parity group in which only one block of error has occurred. That is, the value a _{(n, j)} of the block n of the disk j is obtained using the following equation (3 ₎ .

Then, the controller 4 decodes the block n of the disc i using the horizontal parity group for the block n of the disc j obtained in step 306 in step 306. That is, the value a _{(n, i)} of the block n of the disk i is obtained using the following equation (4 ₎ .

In step 308, it is determined whether m &lt; (N-1). If so, the process proceeds to step 310 and m = m + 1.

In the following example, FIG. 19 shows a process of recovering data in the event of an error in two disks. The data recovery process in the following example will be described with reference to FIGS. 20A to 20G. FIGS. 20A to 20G are diagrams for explaining a data restoration process according to the DH scheme when two disk failures occur. In FIGS. 20A to 20G, as shown in FIG. 14, the second disk d1 (i = 1) and the fourth disk d3 (j = 3) Giving.

If N = 7, error recovery method based on DH method in case of error in two disks

The matrix shown in FIG. 14 is constructed by calculating horizontal parity and diagonal parity values for a given data value in the form of a disk array when N = 7.

The matrix of FIG. 20A shows a situation in which the second and fourth disks in the disk array used in FIG. 14 are in error. That is, i = 1 and j = 3, and thus k = 2.

And n = N-1-k-k * m mod N = 7-1-2-2m mod7 = 4-2m mod7.

Therefore, the equation (3) in step 304 of FIG. 19 for obtaining the value of the block n of the disk j is expressed by the following equation (5)

The equation (4) in the step 306 of FIG. 19 for obtaining the value of the block n of the disk i becomes as shown in the following equation (6).

Accordingly, when m = 0, the equations (5) and (6) are expressed as follows.

a _(4,3) = a _(5,2) a _(3,4) a _(2,5) a _(1,6) a _(0,0)

= 1 0 0 One 1 = 1

a _{(4, 1)} = a _(4, 0 ₎ a _(4,2) a _(4,3) a _{(4, 4)} a _(4,5) a _(4,6)

= 0 0 One 0 One 1 = 1

The a _(4,3) is the fifth block (n = 4) of the fourth disk (j = 3) which is in a fail state and its value is obtained by XOR of its diagonal parity groups. The value of a _{(4, 3)} is 1. The a _(4,1) is the fifth block (n = 4) of the second disk (i = 1 ₎ in the fail state, and it is found that the value is obtained by the XOR of the horizontal parity groups. The value of a _(4,3) is also 1. In the matrix of FIG. 20B, a data value 1,1 recovered by using a diagonal parity group and a horizontal parity group in the fifth block (n = 4) of the fourth and second disks (j = 3, i = 1) .

When m = 1, the equations (5) and (6) are expressed as follows.

a _(2,3) = a _(5,0) a _(4,1) a _(3,2) a _{(1, 4)} a _(0,5)

= 0 One 0 One 1 = 1

a _(2,1) = a _(2,0) a _(2,2) a _(2,3) a _(2,4) a _(2,5) a _(2,6)

= 1 One One 0 0 0 = 1

In the matrix of FIG. 20C, the third block (n = 2) of the fourth and second disks (j = 3, i = 1) failing in the disk array is processed horizontally And the data value 1,1 recovered using the parity group.

When m = 2, the equations (5) and (6) are expressed as follows.

a _{(0, 3)} = a _{(5, 5)} a _(4,6) a _(3,0) a _(2,1) a _(1,2)

= 0 One 0 One 1 = 1

a _{(0, 1)} = a _{(0, 0)} a _(0,2) a _{(0, 3)} a _(0,4) a _(0,5) a _(0,6)

= 1 One One 0 One 0 = 0

20d, the first blocks (n = 0) of the fourth and second disks (j = 3, i = 1) failing in the disk array are processed horizontally Data values 1 and 0 recovered using the parity group are shown.

When m = 3, the above equations (5) and (6) are expressed as follows.

a _(5,3) = a _(4,4) a _(3,5) a _(2,6) a _(1,0) a _(0,1)

= 0 One 0 0 0 = 1

a _{(5, 1)} = a _{(5 ,} 0 ₎ a _(5,2) a _(5,3) a _(5,4) a _{(5, 5)} a _(5,6)

= 0 One One 0 0 1 = 1

In the matrix of FIG. 20E, the sixth block (n = 5) of the fourth and second disks (j = 3, i = 1) failing in the disk array is processed horizontally And the data value 1,1 recovered using the parity group.

When m = 4, the above equations (5) and (6) are expressed as follows.

a _{(3, 3)} = a _{(5, 1)} a _(4,2) a _(2,4) a _(1,5) a _(0,6)

= 1 0 0 0 0 = 1

a _{(3, 1)} = a _{(3, 0)} a _(3,2) a _{(3, 3)} a _(3,4) a _(3,5) a _(3,6)

= 0 0 One 0 One 0 = 0

20F, the fourth block (n = 3) of the fourth and second disks (j = 3, i = 1) which are in a fail state in the disk array through the process of m = Data values 1 and 0 recovered using the parity group are shown.

When m = 5, the above equations (5) and (6) are expressed as follows.

a _(1,3) = a _(5,6) a _(4,0) a _{(3, 1)} a _(2,2) a _(0,4)

= 1 0 0 One 0 = 0

a _{(1, 1)} = a _{(1, 0)} a _(1,2) a _{(1, 3)} a _{(1, 4)} a _(1,5) a _(1,6)

= 0 One 0 One 0 1 = 1

In the matrix of FIG. 20G, the second block (n = 1) of the fourth and second disks (j = 3, i = 1) failing in the disk array is processed horizontally And the data values 0 and 1 recovered using the parity group are shown. Referring to FIG. 20G, it can be seen that the data is completely recovered since it is the same as the first disk array, that is, the matrix shown in FIG.

Hereinafter, the DH2 technique, which is another embodiment of the present invention, will be described with reference to FIGS. 2, 4, 8 to 10, 15 to 18, 21, and 22A to 22G.

DH2 technique

2 is a block diagram of a disk array implemented by the DH2 technique according to another embodiment of the present invention. Referring to FIG. 2, in the block configuration of the disk array implemented by the DH2 scheme, the (N + 1) -th disk 8-n and the buffer 6-n corresponding to the disk 8-n You can see that it is added. An I / O bus 12-n is connected between the controller 4 and the buffer 6-n and between the disk 8-n and the buffer 6-n. The additional disk 8-n according to the DH2 scheme is used to reduce the bottleneck overhead that may occur in updating the contents of the data disk in the DH scheme. The horizontal parity disk to be.

4 is an exemplary diagram for explaining horizontal and diagonal parity groups and horizontal and diagonal parity blocks according to the DH2 technique.

FIG. 8 is a diagram showing the arrangement of horizontal parity groups and horizontal parity blocks of the DH2 scheme when the number N of disks is 7. FIG. 9 is a diagram showing the arrangement of diagonal parity groups and diagonal parity blocks of the DH2 scheme, FIG. 10 is a diagram showing parity and data arrangement in the DH2 scheme when the number N of disks is 7; FIG.

15 is a flowchart of a parity storage algorithm according to the DH2 technique according to another embodiment of the present invention. FIGS. 16 to 18 are diagrams for explaining a parity storing process according to the DH2 technique when the number N of disks is 7.

The DH2 scheme according to another embodiment of the present invention is a method of arranging horizontal parity blocks on a dedicated horizontal parity disk and distributing oblique parity blocks on the remaining disks.

(4), a horizontal parity block and a group (Definition 5), and a diagonal parity block and a group (Definition 6) are defined with reference to FIGS. 4 and 8 to 10, And the data and placement of the DH2 technique based on the above definitions.

Definition 4: Configuration of DH2 technique

(N-1) * (N + 1) matrix as follows: &lt; EMI ID = 1.0 &gt; As shown in Table 3.

a _(0,0) a _(0,1) ... a _{(0, j)} ... a _{(0, N-1)} a _{(0, N)} a _(1,0) a _(1,1) ... a _{(1, j)} ... a _{(1, N-1)} a _{(1, N)} a _(2,0) a _(2,1) ... a _{(2, j)} ... a _{(2, N-1)} a _{(2, N)} ... ... ... ... ... ... a _{(3, N)} a _{(i, 0)} a _{(i, 1)} ... a _{(i, j)} ... a _{(i, N-1)} a _{(4, N)} ... ... ... ... ... ... ... a _(N-2,0) a _(N-2,1) ... a _{(N-2, j)} ... a _{(N-2, N-1)} a _{(N-2, N)}

Definition 5: Horizontal parity group and block in DH2 scheme

In the matrix a _{(i, j)} representing the disk array defined in Definition 4, each row is defined as an error correction group of horizontal parity (hereinafter abbreviated as a horizontal parity group), and the last disk of each horizontal parity group, +1) th disk (called a horizontal parity group), the XOR value of the remaining blocks of the row is stored. That is, the parity value of each horizontal parity group is stored in blocks corresponding to the matrix a _{(i, N)} . Here, the range of i is 0? I? N-3.

4 shows a disk array implemented with five disks (N = 5) d0 to d4, whereby each of the disks d0 to d4 includes four logical blocks (N-1 = 4) b0 to b3, b4 to b7, ... . The three logical blocks b0 to b2, b4 to b6, ... Each of the horizontal parity groups is a corresponding horizontal parity group. In FIG. 4, reference numeral 30 denoted by a solid line represents a horizontal parity group of the second block b1 as an example. In FIG. 4, hatched blocks denote horizontal parity blocks storing parity values of each horizontal parity group, and the horizontal parity blocks are located on the sixth disk d5. That is, it is a block corresponding to the matrix a _{(i, N)} .

FIG. 8 shows the horizontal parity group numbers (0, 1, 2, 3, 4) in the DH2 scheme in the case of N = 7, and the blocks H0 to H4 indicated by the hatched lines represent the parity blocks of the horizontal parity groups do.

Definition 6: Diagonal parity in the DH2 scheme

It is defined the same as the diagonal parity group and block of the DH scheme defined in Definition 3. Referring to FIG. 4, a reference numeral 32 indicated by a dotted line indicates an example of a second diagonal parity group. Blocks indicated by black dots located in 4 (= N-1) th rows (i = 3) are diagonal parity blocks storing parity values of each diagonal parity group. FIG. 9 shows each of the slanting parity groups in the case of N = 7, and the blocks D0 to D6 indicated by black dots are the parity blocks of the diagonal parity groups.

The remaining blocks excluding the horizontal parity block and the diagonal parity block according to the DH2 scheme defined in the definitions 5 and 6 are data blocks in which actual data is stored. FIG. 10 is a diagram showing parity and data arrangement in the DH scheme in the form of a matrix when the number N of disks is 7. In FIG. 10, H0 to H4 denote horizontal parity blocks of horizontal parity groups (0 to 4), and D0 to D6 denote diagonal parity blocks of diagonal parity groups (0 to 6). Each data block is represented by i, j, where i denotes a horizontal parity group and j denotes a diagonal parity group.

The parity storing algorithm according to the DH2 technique is a method of obtaining a parity value of data blocks in each parity group through an XOR operation, and FIG. 15 is a flowchart of a parity storing algorithm of a DH2 technique according to another embodiment of the present invention. When the (N-1) * (N + 1) disk array is configured as shown in step 200 of FIG. 15, the controller 4 of FIG. 2 performs steps 210 and 220 of FIG. 15 to calculate a horizontal parity value and a diagonal parity value I ask. First, in step 210, a horizontal parity block is encoded using each horizontal parity group 0 to (N-3). More specifically, the controller 4 calculates the horizontal parity values of the corresponding horizontal parity groups using the horizontal parity groups 0 to (N-3), and stores them in the horizontal parity blocks in the horizontal parity dedicated disk. The horizontal parity value stored in the horizontal parity block is obtained by Equation (7).

After step 210, the controller 4 encodes the oblique parity block using the oblique parity groups 0 to (N-1) in step 220. [ More specifically, the controller 4 calculates diagonal parity values of the oblique parity groups using the oblique parity groups 0 to (N-1), and stores them in the corresponding oblique parity blocks. The diagonal parity value stored in the slant parity block is obtained by the following equation (8).

An example of encoding an actual horizontal parity value and a diagonal parity value using Equations (1) and (2) will be described with reference to FIG. 16 to FIG. FIGS. 16 to 18 are diagrams for explaining a parity storing process according to the DH2 scheme when the number N of disks is 7; FIG.

Parity storage method according to DH2 technique when N = 7

The matrix shown in Table 4 shows a matrix representing a disk array of the DH scheme in the case of seven disks, i.e., N = 7, and the blocks in each disk are given matrix numbers to be used in encoding and decoding.

a _(0,0) a _(0,1) a _(0,2) a _{(0, 3)} a _(0,4) a _(0,5) a _(0,6) a _{(0, 7)} a _(1,0) a _(1,1) a _(1,2) a _{(1, 3)} a _{(1, 4)} a _(1,5) a _(1,6) a _(1,7) a _(2,0) a _(2,1) a _(2,2) a _(2,3) a _(2,4) a _(2,5) a _(2,6) a _(2,7) a _(3,0) a _{(3, 1)} a _(3,2) a _{(3, 3)} a _(3,4) a _(3,5) a _(3,6) a _{(3, 7)} a _(4,0) a _(4,1) a _(4,2) a _(4,3) a _{(4, 4)} a _(4,5) a _(4,6) a _(4,7) a _(5,0) a _{(5, 1)} a _(5,2) a _(5,3) a _(5,4) a _{(5, 5)} a _(5,6) a _(5,7)

FIG. 16 shows a state where arbitrary data of binary numbers are stored in each data block in a matrix expressed as Table 4. In the empty blocks indicated by shading in the last disk (horizontal dedicated parity disk), horizontal parity values , Diagonal parity values will be stored in empty blocks indicated by black dots after XOR operation for each group based on Equation (7) and Equation (8).

First, a horizontal parity value of each horizontal parity block according to the DH2 technique is calculated using Equation (7).

H ₀ = a _(0,7) = a _(0,0) a _(0,1) a _(0,2) a _{(0, 3)} a _(0,4) a _(0,5) a _(0,6)

= 1 0 One One 0 One 0 = 0

H ₁ = a _(1,7) = a _{(1, 0)} a _(1,1) a _(1,2) a _{(1, 3)} a _{(1, 4)} a _(1,5) a _(1,6)

= 0 One One 0 0 0 1 = 1

H ₂ = a _(2,7) = a _(2,0) a _(2,1) a _(2,2) a _(2,3) a _(2,4) a _(2,5) a _(2,6)

= 1 One One 0 0 0 0 = 1

H ₃ = a _(3,7) = a _(3,0) a _{(3, 1)} a _(3,2) a _{(3, 3)} a _(3,4) a _(3,5) a _(3,6)

= 0 0 One One 0 One 0 = 1

H ₄ = a _(4,7) = a _(4,0) a _(4,1) a _(4,2) a _(4,3) a _{(4, 4)} a _(4,5) a _(4,6)

= 0 One 0 One 0 One 1 = 0

17 In the above equation (7) to each of the horizontal parity block obtained after the value of the determined horizontal parity DH2 technique based on _{a (0,7), a (1,7} ), a (2,7), a (3, _{7) and} a _(4,7) , respectively.

_(5,0), a _(5,1), a _(5,2), a _{(5,3), and} a _(5,4) using the equation (8 _{) ,} a _{(5, 5)} ).

D ₀ = a _(5,0) = a _(4,1) a _(3,2) a _(2,3) a _{(1, 4)} a _(0,5)

= 1 0 One One 1 = 0

D ₁ = a _(5,1) = a _(4,2) a _{(3, 3)} a _(2,4) a _(1,5) a _(0,6)

= 0 One 0 0 0 = 1

D ₂ = a _(5,2) = a _(4,3) a _(3,4) a _(2,5) a _(1,6) a _(0,0)

= 1 0 0 One 1 = 1

D ₃ = a _(5,3) = a _(4,4) a _(3,5) a _(2,6) a _(1,0) a _(0,1)

= 0 One 0 0 0 = 1

D ₄ = a _(5,4) = a _(4,5) a _(3,6) a _(2,0) a _(1,1) a _(0,2)

= 1 0 One One 1 = 0

D ₅ = a _{(5, 5)} = a _{(4, 6)} a _(3,0) a _(2,1) a _(1,2) a _{(0, 3)}

= 1 0 One One 1 = 1

D ₆ = a _(5,6) = a _(4,0) a _{(3, 1)} a _(2,2) a _{(1, 3)} a _(0,4)

= 0 0 One 0 0 = 1

In FIG. 18, the horizontal and diagonal parity values of the DH2 technique are obtained through the above-described processes, and then stored in the respective horizontal and diagonal parity blocks. That is, FIG. 18 shows an example of parity and data arrangement according to the DH2 scheme of the present invention when N = 7.

Next, a decoding method of the DH2 technique according to another embodiment of the present invention, that is, a method of recovering data on a corresponding disk in the event of a disk error will be described.

The basic idea of the data recovery method of the corresponding disk according to the DH2 technique is as follows. When one disk fails, it is easily recovered by using horizontal parity or diagonal parity. When errors occur in the two disks, diagonal parity and horizontal parity Is repeatedly applied to recover all the blocks of the two disks. In a disk array made up of (N + 1) number N of prime numbers, when only one block of the horizontal parity group is in error, the remaining blocks can be recovered by XORing. That is, when N blocks among the (N + 1) blocks constituting the horizontal parity group are complete, the erroneous disk block can be recovered.

A diagonal parity group consists of (N-1) blocks, which are distributed on different disks. In the DH2 technique, there are two cases where an error occurs in two disks. That is, an error may occur in a horizontal parity disk having a horizontal parity block and another disk, or an error may occur in two disks except the horizontal parity disk. When a horizontal parity disk is included, the horizontal parity disk is recovered as in the process of calculating the horizontal parity value according to Equation (7) after restoring each block of the erroneous disk using the diagonal parity group.

If there is an error in two disks except for a horizontal parity disk, that is, if there are two disk errors in N disks, at least one error occurred in only one block among the oblique parity groups. Therefore, if restoring it, the rest of the N blocks of the horizontal parity group including the block can be recovered. Since the restored one block is again one block of the oblique parity group, the rest of the failed parity blocks of the oblique parity group can be recovered and applied to all the blocks in the same manner. In this way, it is possible to recover all errors in any two disks in a disk array made up of a few N pieces.

21, a method of decoding a DH2 technique will be described below. First, when a disc i and a disc j have an error, k, which is a difference value of the disc, is obtained. Then, a disc j (i) belonging to a diagonal parity group of a diagonal parity block of the disc Lt; / RTI &gt; Then, the block of the disk i is recovered through the horizontal parity group including the block of the disk j, and the process is repeatedly performed to recover all the blocks of the failed two disks.

A method for restoring all the blocks of a corresponding disk in which errors have occurred by the controller 4 of FIG. 2 using the DH2 technique according to another embodiment of the present invention will be described in detail with reference to FIG. 21 is a flowchart of a decoding algorithm of the DH2 scheme when two discs fail according to an embodiment of the present invention. In Fig. 21, the following assumption is made.

Assumption: Error occurs on disk i and disk j (0≤i <j≤ (N-1))

The controller 4 of Fig. 2 sets k = j-i and m = 0 in step 400 of Fig. That is, when the disk i and the disk j fail, k is obtained as a difference value of the disk, and a variable m for initializing the block restoring process of the failed disks is initialized to zero.

Then, in step 402, the following n value is obtained.

n = N-1-k-m * k mod N

N is a fail block value of a diagonal parity group in which only one block of error has occurred as described above in the DH scheme. Then, in step 404, the controller 4 decodes the block n of the disk j using the slant parity group in which only one block of error has occurred. That is, the value a _{(n, j)} of the block n of the disk j is obtained using the following equation (9 ₎ .

Then, the controller 4 determines in step 406 whether n = (N-2). If n = (N-2), the process proceeds to step 408. In step 408, the block n of the disc i is decoded using the horizontal parity block for the block n of the disc j obtained in step 404. In this case, the value a _{(n, i)} of the block n of the disc i is obtained using the following equation (10 ₎ .

If n = (N-2) in step 406, the controller 4 proceeds to step 410. In step 410, the block N-2 of the disk i is decoded using the oblique parity block and the horizontal parity block. In this case, the value a _{(n, i)} of the block (N-2) of the disk i is obtained using the equation (11 ₎ .

The controller 4, which has performed steps 408 and 410, then proceeds to step 412. In step 412, it is determined whether or not m &lt; (N-1). In step 414, m = m + 1 is repeated.

In the following example, a process of recovering data in the event of an error occurs in two disks using FIG. 21. The data recovery process in the following example will be described with reference to FIGS. 22A to 22G. FIGS. 22A to 22G are diagrams for explaining a data recovery process according to the DH2 scheme when two disk fail modes are performed. In FIGS. 22A to 22G, as shown in FIG. 18, the second disk d1 (i = 1) and the fourth disk d3 (j = 3) Giving.

When N = 7, if error occurs in two disks, error recovery method according to DH2 technique

The matrix shown in FIG. 18 is constructed by calculating horizontal parity and diagonal parity values for a given data value in the form of a disk array when N = 7.

The matrix of FIG. 22A shows a situation where the second and fourth disks in the disk array used in FIG. 18 have failed. That is, i = 1 and j = 3, and thus k = 2.

And n = N-1-k-k * m mod N = 7-1-2-2m mod7 = 4-2m mod7.

Therefore, the equation (9) in step 404 of FIG. 21 for obtaining the value of the block n of the disk j is expressed by the following equation (12)

Equation (10) in step 408 of FIG. 21 for obtaining the value of block n of disk i is expressed by Equation (13).

However, when n = (N-2), the equation (11) in step 410 is expressed by the following equation (14).

Accordingly, when m = 0, the equations (12) and (13) are expressed as follows.

a _(4,3) = a _(5,2) a _(3,4) a _(2,5) a _(1,6) a _(0,0)

= 1 0 0 One 1 = 1

a _{(4, 1)} = a _(4, 0 ₎ a _(4,2) a _(4,3) a _{(4, 4)} a _(4,5) a _(4,6) a _(4,7)

= 0 0 One 0 One One 0 = 1

The a _(4,3) is the fifth block (n = 4) of the fourth disk (j = 3) which is in a fail state and its value is obtained by XOR of its diagonal parity groups. The value of a _{(4, 3)} is 1. The a _(4,1) is the fifth block (n = 4) of the second disk (i = 1 ₎ in the fail state, and it is found that the value is obtained by the XOR of the horizontal parity groups. The value of a _(4,3) is also 1. In the matrix of FIG. 22B, the data values 1,1 recovered by using the oblique parity group and the horizontal parity group are used as the fifth blocks (n = 4) of the fourth and second disks (j = 3, i = 1) .

When m = 1, the equations (12) and (13) are expressed as follows.

a _(2,3) = a _(5,0) a _(4,1) a _(3,2) a _{(1, 4)} a _(0,5)

= 1 One One 0 1 = 0

a _(2,1) = a _(2,0) a _(2,2) a _(2,3) a _(2,4) a _(2,5) a _(2,6) a _(2,7)

= 1 One 0 0 0 0 1 = 1

In the matrix of FIG. 22C, the third block (n = 2) of the fourth and second disks (j = 3, i = 1) failing in the disk array is processed horizontally And the data values 0 and 1 recovered using the parity group are shown.

When m = 2, the equations (12) and (13) are expressed as follows.

a _{(0, 3)} = a _{(5, 5)} a _(4,6) a _(3,0) a _(2,1) a _(1,2)

= 0 One 0 One 1 = 1

a _{(0, 1)} = a _{(0, 0)} a _(0,2) a _{(0, 3)} a _(0,4) a _(0,5) a _(0,6) a _{(0, 7)}

= 1 One One 0 One 0 0 = 0

(N = 0) of the fourth and second disks (j = 3, i = 1) failing in the disk array through the process of m = 2 in the matrix of FIG. Data values 1 and 0 recovered using the parity group are shown.

(n-2) when m = 3, so that the parity of the failed parity block a ₍ n-1) becomes N = N-1-kk * m mod N = 7-1-2-2 * 3 mod7 = _5,1) is decoded, Equation (14) applied in step 410 of FIG. 21 is cited.

That is, when m = 3, the equations (12) and (14) are expressed as follows.

a _(5,3) = a _(4,4) a _(3,5) a _(2,6) a _(1,0) a _(0,1)

= 0 One 0 0 0 = 1

a _{(5, 1)} = (a _{(5, 0)} a _(5,2) a _(5,3) a _(5,4) a _{(5, 5)} a _(5,6) )

(a _{(0, 7)} a _(1,7) a _(2,7) a _{(3, 7)} a _(4,7) )

= (1 One One 0 0 One) (0 One One One 0) = 1

(N = 5) of the fourth and second disks (j = 3, i = 1) which are in a fail state in the disk array through the process of m = 3 in the matrix of FIG. And the data value 1,1 recovered using the parity group.

When m = 4, the following equations (12) and (13) are expressed as follows.

a _{(3, 3)} = a _{(5, 1)} a _(4,2) a _(2,4) a _(1,5) a _(0,6)

= 1 0 0 0 0 = 1

a _{(3, 1)} = a _{(3, 0)} a _(3,2) a _{(3, 3)} a _(3,4) a _(3,5) a _(3,6) a _{(3, 7)}

= 0 One One 0 One 0 1 = 0

22F, the fourth block (n = 3) of the fourth and second disks (j = 3, i = 1) which are in a fail state in the disk array through the process of m = Data values 1 and 0 recovered using the parity group are shown.

When m = 5, the following equations (12) and (13) are expressed as follows.

a _(1,3) = a _(5,6) a _(4,0) a _{(3, 1)} a _(2,2) a _(0,4)

= 1 0 0 One 0 = 0

a _{(1, 1)} = a _{(1, 0)} a _(1,2) a _{(1, 3)} a _{(1, 4)} a _(1,5) a _(1,6) a _(1,7)

= 0 One 0 0 0 One 1 = 1

22G, the second block (n = 1) of the fourth and second disks (j = 3, i = 1) failing in the disk array is subjected to a process of m = And the data values 0 and 1 recovered using the parity group are shown. Referring to FIG. 22G, since it is the same as the first disk array, that is, the matrix shown in FIG. 18, it can be seen that the data is completely recovered.

The DH method according to the embodiment of the present invention and the error recovery method according to the DH2 method have parallelism, which is one of the advantages of the present invention. The parallelism of the error recovery method means that the recovery process can be performed in parallel, not the sequential process. That is, the error recovery method can be performed in both directions (beginning and end) simultaneously. This will be described in detail with reference to FIG.

FIG. 23 is an exemplary diagram for explaining parallelism of the error recovery method according to the embodiment of the present invention, where N = 7 is used as an example of an error recovery process according to the DH scheme. When an error occurs in the second disk (i = 1) and the fourth disk (j = 3), in the present invention, the sequence shown in FIG. 23, that is, ① → ② → ③ → ④ → ⑤ → ⑥ → ⑦ → ⑧ → ⑨ → ⑩ → ⑪ → ⑫. However, this recovery process may be reversed. That is, the corresponding block (the second block) of the second (i = 2) disk can be found by using the (j + 1) th disk, that is, the shaded parity block of the fifth disk. The corresponding block is a block 12 as shown in FIG. ⑪ Block can be recovered by using horizontal parity group of restored ⑫ block. Then, using the diagonal parity group of the restored ⑪ block, the ⑩ block can be recovered. In other words, it is restored in the order of ⑫ → ⑪ → ⑩ → ⑨ → ⑧ → ⑦ → ⑥ → ⑤ → ④ → ③ → ② → ①. The reverse order of the recovery order and the intermediate process are not superimposed. Therefore, if the process is performed in both directions at the same time, the recovery time can be reduced by up to half.

The performance evaluation of the DH and DH2 schemes according to the embodiment of the present invention will be described below in comparison with other schemes (two-dimensional parity scheme, EVENODD scheme). The performance evaluation indexes are exemplified by the following (1) to (4).

(1) Mean Time to Data Loss (MTTDL)

(2) Parity disk overhead

(3) Update penalty

(4) Group size

In the following tables and referenced drawings, the two-dimensional parity scheme will be expressed in 2D, the EVENODD scheme will be expressed as EO, the DH scheme as DH, and the DH2 scheme as DH2.

First, a comparison of the average time for data loss of each technique (1) will be described.

MTTDL means the average time for data loss. In a method that can be recovered when an error occurs in two disks, it can be expressed by the following equation (15).

Here, MTTF (disk) means the mean time to failure in one disk, MTTR is the mean time to reconstruction (reconstruction), N is the total number of disks, And G represents the size of the error correction group. Although the MTTDL is the most important performance criterion, the actual value is not meaningful for performance evaluation because the time is usually over several thousand years. For example, assuming that 200,000 hours of MTTF (disk), 20,000 hours of MTTF (disk2), 2,000 hours of MTTF (disk3), and 1 hour of MTTR are used, when 100 data disks are used in a two- The total number of disks N is 120 and the group size G is 11. Therefore, the MTTDL is about 85,000 years old. In MTTDL, MTTF (disk) and MTTR are constants, so MTTDL is inversely proportional to the square of the total number of disks N constituting the disk array and the size G of the error correction group. Therefore, MTTTDL can be expressed as MTTDL _S and MTTDL _{SI, which} is an inverse value thereof, can be simplified as shown in Equation (16) below.

Table 6 shows MTTDL _S according to a given number of data discs as shown in Table 5, and FIG. 24 shows MTTDL _SI as a graph.

2D EO DH DH2 Number of data discs m m m m + 1 Number of parity disks 2 2 2 Total number of disks m + 2 m + 2 m + 3

2D EO Number of data discs m m Total number of disks (N) Size of error correction group (G) MTTDL _S DH DH2 Number of data discs m m + 1 Total number of disks (N) m + 2 m + 3 Size of error correction group (G) m + 2 MTTDL _S

Next, (2) parity disk overhead of each technique will be compared.

The parity disk overhead is expressed by the following equation (18) as the ratio of the number of data disks to the number of parity disks.

Parity The small disk overhead means that you can store a relatively large amount of data when you configure a disk array with the same number of disks. If you use the same number of data disks, the larger the parity disk overhead, The efficiency of use of the disk is reduced. That is, the parity disk overhead can be a criterion for evaluating the price-to-performance ratio and is an index indicating the efficiency of the number of disks. Table 7 shows the parity disk overhead of each technique when the number of data discs is m. It can be seen that the overhead of the two-dimensional parity technique is greatest when a disk array is constructed using the same number of data discs. That is, the parity overhead of the two-dimensional parity scheme is about And the efficiency of disk utilization is lowered. Therefore, the efficiency of disk utilization is lower than that of other schemes.

2D EO DH DH2 Number of data discs m m m m + 1 Number of parity disks 2 2 2 Parity disk overhead

Next, we compare (3) update penalty of each technique.

The update cost represents the number of parity disks to be accessed when updating the data disk information in the disk array. The optimal update cost is 2 in the technique that can recover from errors in two disks. However, if the update cost is high, additional parity disk access is required to update the data disk, which may cause performance degradation in the write operation. For the two-dimensional parity and DH2 schemes, the optimal update burden cost condition is satisfied, whereas the EVENODD and DH schemes are larger than the two-dimensional parity and DH2 schemes. In the case of the EVENODD scheme, all the oblique parity blocks need to be updated when data blocks corresponding to the slant value S are updated as shown in FIG. 25, so there is an overhead in the update burden cost. That is, when the disk array is constituted by m data disks, the number of parity disks to be accessed when updating the information of the data disk is 2, but the number of parity blocks is one for the horizontal parity block, 1), so the parity block needs to be updated m times. In other cases, the parity block is accessed twice.

In addition, in the DH method, not only the horizontal parity block and the oblique parity block need to be updated at the time of updating all the data blocks, but the parity value of the parity blocks must be maintained. FIG. 26 is a representation of a Pareto block to be updated when a hatched block is updated.

Table 8 below compares the update burden cost for each technique. In the EVENODD technique, the overhead described above is represented by?. Therefore, it can be seen that the two-dimensional parity scheme and the DH2 scheme have the optimum update cost.

2D EO DH DH2 Renewal cost 2 2 + alpha 3 2

Finally, we compare (4) the group size of each technique.

The group size, which refers to the size of an error correcting group, is defined as the set of disks that must be accessed while recovering from an error in one disk. The group size is meaningful because the reconstruction period linearly increases as the number of disks to be read back at the time of recovery increases. Also, the MTTDL (the Mean Time To Date Loss) is in inverse proportion to the group size, so the group size should be small. For RAID level 6, there are two group sizes because two parity blocks must have a parity value for one data block. That is, horizontal parity and vertical parity for the two-dimensional parity scheme, horizontal parity and diagonal parity error correction groups for the EVENODD scheme, DH scheme, and DH2 scheme are respectively distinguished and the names of the respective schemes are expressed in superscripts of G, Let the English header of G be expressed as a subscript of G. And the absence of subscripts means the average of the two group sizes. First, when considering the group size of the two-dimensional parity scheme, when the number of data disks is m, the horizontal parity group size And vertical parity group size The or And average The And summarizing it to be. here, Means an integer not greater than X, Means an integer not less than X. In the EVENODD technique, the horizontal parity group size Is m + 1 and the diagonal group size Is 2 (m-1) +1, end to be. DH technique (M + 2) &lt; / RTI &gt; (M + 1), the average The , The DH2 technique And (M + 3) and (m + 1), respectively, The to be. This is summarized in Table 9 below, and in FIG. 27 a graph of the group size for several examples is shown. Referring to FIG. 27, it can be seen that the group size of the two-dimensional parity scheme is the smallest, and the EVENODD scheme is the largest due to the overhead of the slanting value S. FIG.

2D EO DH DH2 Number of data discs m m m m + 1 GS average

As a result, the DH scheme, which is an embodiment of the present invention, can be recovered by repeatedly applying diagonal parity and horizontal parity even if any two disks in the disk array having a small number of N fail, and by distributing the parity blocks, The performance degradation factor was removed. In addition, there is a peak that can reduce the recovery time by processing the disk failure recovery process in both directions in parallel. However, when updating the contents of the data disk, three disk accesses are required, which may cause degradation in performance. However, it can be overcome through disk caching or other methods. As shown in FIG. 1, in the disk array system of the present invention, buffers 6-0 to 6- (n-1) are respectively provided in the disks 8-0 to 8- (n-1). These buffers 6-0-6- (n-1) are used for buffering and caching. Write buffering, also referred to as asynchronous write, is a method of recognizing user write requests before writing to disk. This technique reduces the response latency experienced by the user, thereby alleviating the load . As a technique of the write buffering, there is a method of grouping a series of write requests into one group and processing them. In addition, since it is not necessary to read the existing parity data by caching the recently updated parity, the disk access required for small writing can be reduced to 3 to 2 times.

The DH2 scheme, which is another embodiment of the present invention, is similar to the structure in the DH scheme because diagonal parity blocks are distributed on a data disk. However, by disposing parity blocks on one parity disk, the problem of the DH scheme, In addition, the cost of updating the parity disk should be reduced to two. Although the DH2 technique may cause a spare block in a horizontal parity disk, it may cause a problem in disk efficiency. However, if the block is applied to a method for solving a small write problem, It can increase the usage.

While the present invention has been described in connection with certain exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. Therefore, the scope of the present invention should not be limited by the described embodiments but should be determined by the equivalents of the claims and the claims.

As described above, the present invention can recover and optimize overhead by repeatedly applying diagonal parity and horizontal parity even if an error occurs in any two disks in a disk array made up of a few N pieces. We also solve the bottleneck by distributing the parity blocks. Thus improving system performance. In addition, the parallelism of the recovery process can be used to recover from both directions, which may shorten the recovery time.

Claims (24)

CLAIMS 1. A method for recovering data in parity storage and disk failure in an external storage subsystem, comprising: (N-1) * N matrix by making a number of N disks and each disk of the disks to be (N-1) block units, and blocks of each row of the matrix are divided into horizontal parity Group is defined as a diagonal parity group, and blocks of cyclic configuration are defined as diagonal parity groups in the upper right diagonal direction of the matrix, and horizontal parity blocks are defined as diagonal directions in the first block of the immediately preceding (N-1) (N-1) -th block of each disk; A parity storing step of performing XOR operation on the data values of each of the horizontal and diagonal parity groups and storing the data values in the horizontal and diagonal parity blocks of the corresponding group; If an error occurs in the two disks, restores the fail block using a diagonal parity group including one fail block, and then restores the fail block of the horizontal parity block using a horizontal parity group of the recovered fail block, And recovering all the fail blocks of the two failed disks by repeatedly applying the above process. The method of claim 1, further comprising the step of restoring the corresponding blocks of the erroneous disk using the remaining blocks of the horizontal parity groups when an error occurs in one disk. 2. The method of claim 1, wherein the (N-1) * N matrix is a _{(i, j)} type representing a value of a logical block i of a disk j where i is 0? I? N-2 and j is 0 I? N-1), the horizontal parity blocks are a _{(i, N-2-i)} . 4. The method of claim 3, wherein the diagonal parity blocks are a _{(N-2, j)} . The method of claim 4, wherein the exclusive OR computation is performed on the horizontal parity blocks a _{(i, N-2-i) according} to Equation (19 ₎ to store a horizontal parity value. 5. The method of claim 4, wherein the exclusive OR computation is performed on the oblique parity blocks a _{(N-2, j) according to} the following equation (20 ₎ to store the oblique parity values. The method of claim 4, wherein said case is an error on the disk and disk i j (0≤i <j≤ (N- 1)), to the error block of the disk a j _{(n, j)} Equation RTI ID = 0.0 &gt; 21, &lt; / RTI &gt; n = N-1-k-m * k mod N, k = j-i, m is from 0 to N-2. The method of claim 4, wherein said case is an error on the disk and disk i j (0≤i <j≤ (N- 1)), the error block of the disk a i _{(n, i)} Equation The original data is restored based on the original data. n = N-1-k-m * k mod N, k = j-i, m is from 0 to N-2. CLAIMS 1. A method for recovering data in parity storage and disk failure in an external storage subsystem, comprising: 1) * (N + 1) matrix by making N + 1 (N is a prime number) disks and each disk of the disks to be (N-1) block units, Blocks of each row of the matrix are defined as a horizontal parity group, and blocks of cyclic configuration are defined as a diagonal parity group in the upper right diagonal direction of the matrix except for the block of the last (N + 1) th disk, Arranging blocks in blocks of the last (N + 1) th disk and disposing oblique parity blocks in (N-1) th blocks of each disk; A parity storing step of performing XOR operation on the data values of each of the horizontal and diagonal parity groups and storing the data values in the horizontal and diagonal parity blocks of the corresponding group; If an error occurs in the two disks, restores the fail block using a diagonal parity group including one fail block, and then restores the fail block of the horizontal parity block using a horizontal parity group of the recovered fail block, And recovering all the fail blocks of the two failed disks by repeatedly applying the above process. 10. The method of claim 9, further comprising the step of restoring the corresponding blocks of the erroneous disk using the remaining blocks of the horizontal parity groups when an error occurs in one disk. The method of claim 9, wherein the (N-1) * (N + 1) matrix is a _{(i, j)} , j is 0? _{i? N)} , the horizontal parity blocks are a _{(i, N)} . 12. The method of claim 11, wherein the diagonal parity blocks are a _{(N-2, i)} . 12. The method of claim 11, wherein the exclusive OR computation is performed on the horizontal parity blocks a _{(i, N) according} to Equation (23 ₎ to store a horizontal parity value. 12. The method of claim 11, wherein the exclusive OR computation is performed on the diagonal parity blocks a _{(N-2, i) according} to Equation (24 ₎ to store the oblique parity values. 12. The method of claim 11, wherein said case is an error in the disk and the disk i j (0≤i <j≤ (N- 1)), to the error block of the disk a j _{(n, j)} Equation 25, &lt; / RTI &gt; n = N-1-k-m * k mod N, k = j-i, m is from 0 to N-2. 12. The method of claim 11, wherein the errored blocks a _{(n, i)} of the disk i are subjected to the following equations if an error occurs in disk i and disk j (0? I <j? 26 and (27) (where n = (N-2)). n = N-1-k-m * k mod N = N-2, k = j-i, m = 0 to N-2. , n = N-1-km * k mod N = N-2, k = ji, m is from 0 to N-2. An apparatus for recovering data in parity storage and disk failure in an external storage subsystem, the apparatus comprising: (N-1) * N matrix by making a number of N disks and each disk of the disks be (N-1) block unit, blocks of each row of the matrix are defined as a horizontal parity group, Blocks of circulating configuration are defined as a diagonal parity group, and the horizontal parity blocks are arranged one by one on each disk so as to be oblique to the first block of the immediately preceding (N-1) th disk The disk array of the structure in which the oblique parity blocks are arranged in the (N-1) th block of each disk, Performing XOR operation on the data values of each of the horizontal and diagonal parity groups to store horizontal and vertical parity values in horizontal and diagonal parity blocks of the group, respectively; If an error occurs in the two disks, restores the fail block using a diagonal parity group including one fail block, and then restores the fail block of the horizontal parity block using a horizontal parity group of the recovered fail block, And a controller for repeatedly applying the above process to recover all the fail blocks of the two failed disks. 18. The apparatus of claim 17, wherein when the error occurs in one disk, the controller recovers the corresponding blocks of the erroneous disk using the remaining blocks of the horizontal parity groups. 18. The apparatus of claim 17, wherein buffers for buffering and caching data of the disk are provided between the disks of the disk array and the controller to reduce disk access in the controller when updating the contents of the data disk, . An apparatus for recovering data in parity storage and disk failure in an external storage subsystem, the apparatus comprising: 1) * (N + 1) matrix by making N + 1 (N is a prime number) disks and each disk of the disks to be (N-1) block units, and each row Blocks are defined as a horizontal parity group, and blocks of cyclic configuration are defined as diagonal parity groups in the upper right diagonal direction of the matrix excluding the block of the last (N + 1) th disk, and the horizontal parity blocks are defined as the last (N-1) -th disk), and a disk array having a structure in which oblique parity blocks are arranged in (N-1) -th blocks of each disk, Performing XOR operation on the data values of each of the horizontal and diagonal parity groups to store a horizontal parity value and a diagonal parity value in horizontal and diagonal parity blocks of the group, respectively; If an error occurs in the two disks, restores the fail block using a diagonal parity group including one fail block, and then restores the fail block of the horizontal parity block using a horizontal parity group of the recovered fail block, And a controller for repeatedly applying the above process to recover all the fail blocks of the two failed disks. 21. The apparatus of claim 20, wherein, when an error occurs in one disk, the controller recovers the corresponding blocks of the erroneous disk using the remaining blocks of the horizontal parity groups. 21. The apparatus of claim 20, wherein buffers for buffering and caching data of the disk are provided between each disk of the disk array and the controller to reduce disk access in the controller when updating the contents of the data disk, . (N-1) * N matrix by making a number of N disks and each disk of the disks to be (N-1) block units, and blocks of each row of the matrix are divided into horizontal parity Group is defined as a diagonal parity group, and blocks of cyclic configuration are defined as diagonal parity groups in the upper right diagonal direction of the matrix, and horizontal parity blocks are defined as diagonal directions in the first block of the immediately preceding (N-1) (N-1) -th block of each disk, and the data values of each of the horizontal and diagonal parity groups are XORed by the controller, And disk diagonal parity blocks are stored as horizontal and diagonal parity values, respectively. In an external storage subsystem, disk i and disk j are stored in (0? I <j? (N-1) A method for recovering data in case of: A first step of obtaining a difference value k between discs i and j in which the error has occurred and initializing a variable m for repeated application of the block recovery process of the failed discs to 0; _{(N, j)} of a block n (n = N-1-km * k mod N) a _{(n, j)} of the disk j having only one error occurrence in the oblique parity group using the following equation , _{(N, i)} of a disk i having only one error occurrence in a corresponding horizontal parity group after performing the second process using Equation (29 ₎ ; and And repeating the second and third processes while increasing the variable m to N-2. 1) * (N + 1) matrix by making N + 1 (N is a prime number) disks and each disk of the disks to be (N-1) block units, Blocks of each row of the matrix are defined as a horizontal parity group, and blocks of cyclic configuration are defined as a diagonal parity group in the upper right diagonal direction of the matrix except for the block of the last (N + 1) th disk, Blocks are arranged in blocks of the last (N + 1) -th disk, and diagonal parity blocks are arranged in (N-1) -th blocks of each disk, and data of each of the horizontal and diagonal parity groups Values are subjected to an exclusive OR (XOR) operation to store the horizontal and the diagonal parity values in the horizontal and the diagonal parity blocks of the corresponding group, respectively. In the external storage subsystem, when the disk i and the disk j satisfy (0? I <j? 1) Oh A method for recovering data in the occurrence of a flow, comprising: A first step of obtaining a difference value k between discs i and j in which the error has occurred and initializing a variable m for repeated application of the block recovery process of the failed discs to 0; _{(N, j)} of a block n (n = N-1-km * k mod N) a _{(n, j)} of a disk j having only one error occurrence in the oblique parity group using Equation , The value of the block na _{(n, i)} of the disc i having only one error occurrence in the horizontal parity group after the second process is expressed by the following equation (31) (when n ≠ N-2) N-2) is used, And repeating the second and third processes while increasing the variable m to N-2.